Various theories, such as the internal clock theory (Church, 1984) and the behavioral theory of timing (Killeen and Fetterman, 1988), have sought to explain the neural mechanisms underlying time perception. Computational and robotic models have been developed to study these theories, including the pacemaker-accumulator model (Simen et al., 2013) and the memory decay model (Addyman et al., 2011). The pacemaker-accumulator model provides a framework for how time and duration are perceived, insisting that a mechanism in the brain (the pacemaker) sends pulses to an accumulator in the brain that counts the pulses to deduce time. The theory further suggests the presence of a “switch” between the pacemaker and accumulator that activates depending on whether the brain is actively paying attention to time (Simen et al., 2013). In contrast, the memory decay model of time perception posits that our temporal judgments are influenced by the gradual weakening of memory traces. As retention intervals increase, there is a progressive strengthening of central bias, where individuals place greater weight on expected rather than actual duration distributions when perceiving incoming sensory stimuli (Addyman et al., 2011). Review papers like Basgol et al. (2021) have synthesized these works, but there remains a need for a comprehensive framework that exploits temporal information to govern agentic behavior.

In addressing the computational mechanisms underlying temporal processing, the State-Dependent Network (SDN) model (Karmarkar and Buonomano, 2007) demonstrates that temporal information can be encoded through intrinsic neural dynamics via short-term synaptic plasticity and GABA_B-mediated inhibition, rather than dedicated timing mechanisms. This context-dependent framework, wherein temporal encoding varies with the network’s initial state, provides a mechanistic explanation for how internal mental states influence time perception. However, the model’s severe temporal limitations (<500 ms), are validation restricted to simple discrimination tasks, and parameter sensitivity undermines its explanatory power, particularly as its inability to account for longer durations necessitates hybrid approaches that reintroduce the dedicated timing mechanisms it sought to replace.

In the pursuit of a unified model of time perception, numerous studies have revealed striking parallels between numerical and temporal processing, as evidenced by behavioral, neural, and clinical data (Dormal et al., 2006; Feigenson, 2007; Provasi et al., 2011; Dormal and Pesenti, 2012, 2013; Vicario et al., 2013). These parallels, supported by behavioral, neural, and clinical evidence, suggest shared underlying mechanisms that could form the foundation of such a model. Behavioral data indicates that both numerical and temporal judgments rely on Weber’s Law, with discrimination being more straightforward when quantities differ by a larger ratio (Stevens, 1957). Weber’s law states that the just-noticeable difference between two stimuli is proportional to the magnitude of the stimuli (Fechner, 1966). For instance, rats and infants have demonstrated the ability to generalize rules learned in one area, such as time or numbers, to the other (Meck and Church, 1983; de Hevia et al., 2012). However, in the case of infants, similar developmental trajectories are observed during infancy, but divergence emerges in childhood (Odic, 2017).

This highlights the need for a plausible foundational model of perceptual time that can accommodate these developmental deviations. While our current framework is not age-parameterized, it can account for these effects by attributing developmental changes to evolving neural architecture, specifically, changes in the effective number of processors, efficiency, and power consumption. As cortical networks mature and cognitive functions like attention and working memory strengthen, the brain’s capacity to process temporal information becomes more differentiated. Future empirical work could use this framework to map developmental trends in time estimation to underlying neural computation parameters.

Additionally, neuroimaging studies have shown intraparietal sulcus (IPS) activation during both numerical and temporal processing in adults (Dormal et al., 2012; Skagerlund et al., 2016; Hayashi et al., 2013), suggesting that the comorbid deficits in quantity processing observed in clinical disorders like Turner syndrome—linked to spatial reasoning and working memory impairments—may arise from disruptions in the neural mechanisms supporting these overlapping cognitive functions (Vicario et al., 2013). The overall consensus is that the IPS is implicated more strongly in numerical than temporal processing (Rammsayer and Classen, 1997; Nenadic et al., 2003; Mattel and Meck, 2004; Koch et al., 2009), which led to the proposal of a standard magnitude system responsible for processing both time and numbers (Meck and Church, 1983; Walsh, 2003; Cantlon et al., 2009).

Given the findings from IPS and laboratory studies, the correlation between temporal and numerical processing was previously a key foundational component of time perception. However, inconsistencies in subsequent research have ultimately discredited its inclusion in models (Baker et al., 2013; Young and Cordes, 2013; Odic, 2017), highlighting the need for a plausible foundational model for perceptual time that rectifies inconsistencies in existing research.

As research advances in the fields of biology and neuroscience, it is increasingly apparent that the brain’s mechanisms for perceiving time are highly complex, posing significant challenges for developing a comprehensive understanding of these processes. A simplified theoretical model that abstracts the complexities of neural computation and focuses on critical parameters governing the brain’s information processing capacity has the potential to elucidate how computational limitations lead to perceptual time distortions. By building upon fundamental principles of information processing, energy consumption, and physical constraints, such a model can capture the essential aspects of perceptual time.

In this paper we propose a simplified theoretical model, the Perceptual Model of Time, to explore how the brain’s computational limitations might lead to perceptual time distortions. This model abstracts the complexities of neural computations and focuses on key physical parameters that govern the brain’s information processing capacity.

Our model is built upon three fundamental principles:

By acknowledging these principles, we can construct a model that, while simple, captures the essential aspects of how computational limitations affect perceptual time. This approach builds upon the existing body of research synthesized in review papers like Basgol et al. (2021) while providing a novel framework that exploits temporal information to govern agentic behavior.

While traditional frameworks such as the pacemaker-accumulator (Simen et al., 2013) and memory decay models (Addyman et al., 2011) focus on the internal generation of temporal signals or the degradation of memory traces over time, our approach shifts emphasis to the computational constraints that govern overall neural information processing capacity. Rather than relying solely on clock-like mechanisms or passive forgetting, our model incorporates fundamental physical and metabolic constraints—such as parallel processing capabilities, energy consumption, and efficiency factors—to provide a broader, capacity-limited perspective on how time perception emerges from the brain’s underlying information-processing architecture.

We distinguish perceptual time (t’) from inertial time (t) and introduce the following key variables:

I: Total information processed by the brain (bits)

N: Number of processors (e.g., neurons or functional computing units)

P: Power consumption per processor (watts)

η: Efficiency factor (bits/joule)

T: Absolute temperature of the brain (kelvin)

Step 1: Define the maximum computational rate of the brain (R) (in bits/s) as:

Equation 1 represents the total rate at which the brain can process information.

Step 2: Relate perceptual time to the total information processed (I) and the computational rate (R):

This implies that perceptual time is proportional to the total information processed divided by the processing capacity, aligning with our conceptual framework.

Examples:

In the context of perceptual time, the relationship between inertial time and perceptual time can be represented by various ratios.

A 1:1 ratio indicates that 1 s of perceptual time is equivalent to 1 s of inertial time, suggesting a perfect correspondence between the two. However, deviations from this ratio can occur, leading to either a compression or dilation of perceptual time.

When the ratio is 1:0.5, 1 s of perceptual time is equal to 0.5 s of inertial time, indicating a compression of perceptual time (moments feel longer or slower).

Conversely, a ratio of 1:2 represents a dilation of perceptual time, where 1 s of perceptual time is equal to 2 s of inertial time (moments feel shorter or faster).

Landauer’s Principle, proposed by Landauer (1961), states that any logically irreversible manipulation of information, such as the erasure of a bit, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment. More simply put, erasing even a single bit of information—such as resetting a computer memory from “1” to “0”—requires a small amount of energy. This principle establishes a fundamental link between information processing and thermodynamics, with the minimum energy required to erase one bit of information at temperature T given by kTln2, where k is the Boltzmann constant (Landauer, 1961).

To refine our model, we incorporate Landauer’s Principle, which states that erasing or resetting one bit of information requires a minimum amount of energy:

Where:

To incorporate Landauer’s Principle (Equation 3) into the theoretical framework, we need to consider the minimum energy required to process information in the brain. We’ll modify the efficiency factor (η) to account for this minimum energy requirement.

Where:

Step 1: Determine the minimum power required to process information.

Step 2: Modify the efficiency factor (η) to account for the minimum power requirement (Equation 4).

Step 3: Express the total information processed (I) in terms of the information processing rate (If) and inertial time (t).

Step 4: Substitute Equations 5, 6 into Equation 2 for perceptual time (t′).

Step 5: Simplify the Equation 7 by expanding Equation 5.

Condensing Equation 8 we get the final equation:

Units simplify to seconds, confirming dimensional consistency (see Appendix A).

Bremermann’s Limit, proposed by Bremermann (1962), represents the maximum computational speed of a self-contained system in the material universe. This limit is derived from the mass-energy equivalence and Heisenberg’s Uncertainty Principle, and it sets an upper bound on the rate at which information can be processed per unit of energy (Bremermann, 1962).

Bremermann’s Limit is defined as:

Where:

To account for the physical limitations on the brain’s computational speed, we incorporate Bremermann’s Limit (Equation 10) into the theoretical framework. By constraining the efficiency factor (η) using this limit, we ensure that the model adheres to the fundamental principles governing the maximum rate of information processing per unit of energy.

Step 1: Define the total power consumption of the system as:

Equation 11 is power which is equivalent to energy per unit time (watts = joules/s), the total energy consumed over a time interval (Δt) is:

However, Bremermann’s Limit concerns the maximum computational rate at any instant, so in Equation 12 we’ll consider (Δt=1s) second for simplicity:

Step 2: Apply Bremermann’s Limit.

Substitute Equation 13 into Bremermann’s Limit:

Equation 14 represents the maximum computational rate achievable by the system based on its total energy consumption.

Step 3: Constrain the efficiency factor (η).

From Equation 2:

According to Bremermann’s Limit, (R) must satisfy:

Substitute the expressions for (R) (Equation 15) and (R max) (Equation 14) into Equation 16:

Simplify both sides of Equation 17 (N×P) (assuming N×P≠0):

Step 4: Update the Perceptual Time Equation (Equation 2).

The original expression for perceptual time is:

With the constraint on Equation 18, the minimum perceptual time (tmin′) is achieved when (η) is at its maximum value:

Substituting Equation 19 into Equation 2:

Units simplify to seconds, confirming dimensional consistency. (see Appendix A).

Given:

Step 1: Substitute Equation 19 into Equation 9:

Step 2: Simplify Equation 21:

Reduce Equation 22 to get the final comprehensive equation:

Units simplify to seconds, confirming dimensional consistency (see Appendix A).

The proposed theoretical model, which integrates Landauer’s Principle and Bremermann’s Limit, provides a novel perspective on how the brain’s computational limitations may lead to perceptual time distortions. By abstracting the complexities of neural computations and focusing on key parameters governing information processing capacity, this model offers valuable insights into the fundamental physical constraints that shape our perception of time.

The basic model, as described by Equation 2, establishes a direct proportionality between perceptual time (t′) and the total information (I) processed by the brain:t′=IN×P×ηwhere (N) denotes the number of parallel processors, (P) represents the power consumption per processor, and (η) signifies the computational efficiency. This relationship implies that an increase in the cognitive load, manifested as a higher (I) can lead to a dilation of perceptual time within a given inertial time interval. This phenomenon aligns with empirical observations where heightened cognitive engagement results in the underestimation of time duration, as individuals allocate more attentional resources to processing information, thereby reducing their temporal awareness (Castellotti et al., 2022).

Furthermore, the model highlights an inverse relationship between perceptual time with respect to both the number of processors (N) and the efficiency (η). An increase in (N) facilitates parallel processing, effectively distributing the cognitive load and potentially leading to a compression of perceptual time. This is corroborated by neuroimaging studies demonstrating that parallel processing networks in the brain contribute to more efficient task performance and altered time perception (Sigman and Dehaene, 2008). Similarly, higher computational efficiency (η) implies that the brain requires less energy to process a given amount of information, which will result in a compression of perceptual time.

Incorporating Landauer’s Principle introduces a thermodynamic constraint on the minimum energy (Emin) required for information processing:Emin=kTln2where (k) is the Boltzmann constant and (T) is the absolute temperature of the brain. By embedding this principle into the model, we recognize that energy consumption is not merely a biological parameter but is fundamentally limited by thermodynamics. The modified equation (Equation 9) accounts for the energy-temperature dependence, suggesting that increases in brain temperature (T) raise the minimum energy threshold (Emin), potentially leading to a dilation of perceptual time. This theoretical insight is supported by experimental findings indicating that elevated body temperatures can accelerate the subjective passage of time (Hancock, 1993; Behm and Carter, 2020).

Bremermann’s Limit imposes a quantum mechanical ceiling on the rate of information processing, constraining the maximum computational efficiency (ηmax):ηmax=2π×ℏwhere (ℏ) is the reduced Planck constant.

This quantum constraint introduces a lower limit to temporal resolution in cognitive processes, suggesting that our subjective perceptual experience of time is inherently quantized and bounded by the universe’s fundamental properties (Buice and Cowan, 2009; Atmanspacher and Filk, 2002). In turn, this limit underscores that there is an absolute bound on how efficiently energy can be converted into information processing, dictated by fundamental physical constants. The implication is profound: there is a minimum perceptual time (tmin′) necessary for the brain to process a given amount of information (I), precluding the possibility of instantaneous perception (Bruza et al., 2009).

By synthesizing the basic model with both Landauer’s Principle and Bremermann’s Limit, we arrive at a comprehensive equation that captures the complex dependencies of perceptual time:

This final expression emphasizes that perceptual time is a function of inertial time, modulated by the brain’s information processing rate, power consumption, and constrained by both thermodynamic and quantum mechanical limits.

The integration of fundamental physical principles into the model not only bridges the gap between psychology, neurophysiology and physics but also highlights that cognitive processes are ultimately governed by universal laws. The recognition that perceptual time is constrained by Landauer’s Principle and Bremermann’s Limit provides a novel perspective on the limitations of the human brain.

Our theoretical findings resonate with and extend existing research on time perception and cognitive load. Studies have consistently shown that increased cognitive demands can distort time perception, leading to either an underestimation or overestimation of elapsed time (Block et al., 2010). The incorporation of thermodynamic and quantum constraints offers a foundational explanation for these phenomena, rooted in the physical limitations of information processing.

Moreover, the model’s implication that temperature influences perceptual time is supported by experimental work demonstrating that physiological states affecting body temperature can alter time perception (Wearden et al., 2007). By framing these observations within the context of Landauer’s Principle, we provide a thermodynamically grounded rationale for such effects.

Building on this capacity-limited framework, one can draw parallels between biological time perception and the emergent “perceptual time” within artificial intelligence (AI) systems. Just as the brain’s finite information-processing capabilities constrain the subjective flow of time (Panagiotaropoulos et al., 2012; Dormal et al., 2012), advanced AI models configured with hardware, energy budgets, and algorithmic constraints must also operate within strict computational limits. The result is that AI “experiences” a form of time not solely governed by an external clock but by the interplay of processing throughput and energy considerations, akin to the rate-limiting factors in human neural tissue (Simen et al., 2013; Addyman et al., 2011). Though the notion of AI consciousness remains a topic of debate and investigation, these capacity-driven constraints imply that any sufficiently complex system might develop an emergent internal chronometry that parallels human perceptual time (Basgol et al., 2021). In this sense, AI becomes “aware” of temporal progression insofar as it encodes and updates internal states according to a rate of information processing that is fundamentally constrained by power consumption, efficiency, and the number of parallel processing units. Thus, whether in cortical networks or digital architectures, perceptual time can be viewed as an adaptive byproduct of computational limits, providing a unified theoretical perspective on how systems biological or artificial come to register, track, and even subjectively experience the flow of time.

Unlike biological observers, current AI architectures process time exclusively through deterministic clock cycles and algorithmic scheduling; they lack the affective states and memory distortions that generate human temporal illusions. Consequently, any divergence between ‘perceptual’ and inertial time in today’s AI is not phenomenological but purely computational (e.g., variable task-queue latency or throttled throughput). Whether future systems develop a genuinely subjective temporality and thus exhibit a true perceptual inertial gap, remains an open empirical question.

As we begin to integrate neurotechnology more deeply the concept of perceptual time becomes increasingly critical. By directly interfacing with neural pathways, BCIs could augment or even override the brain’s intrinsic temporal dynamics, opening up the possibility of effectively hyper compressing or “freezing” inertial time for the user. In principle, if the processing and resource constraints are optimized correctly, one could create intervals of experience where large amounts of cognitive operations occur while external time appears to stand still.

The proposed theoretical model, which establishes fundamental physical limits on the brain’s computational capacity, raises intriguing questions about the existence of a finite range of computation within which all humans operate. If the brain’s information processing is indeed constrained by thermodynamic and quantum mechanical bounds, as suggested by the integration of Landauer’s Principle and Bremermann’s Limit, it implies that there may be a universal “cognitive envelope” that defines the boundaries of all human thought and perception. Further research and development of the model may elucidate other fundamental physical characteristics of the universe bounded by human perception rather than traditional physics.

While the model offers significant insights, it remains a simplification of the complex neural processes underlying time perception. The brain’s information processing is modulated by a myriad factors, including attention, emotional state, memory, and sensory inputs, which are not explicitly captured in the current framework. Additionally, parameters such as the number of processors (N) and efficiency (η) are treated abstractly, without precise quantification in neurobiological terms.

Future research should aim to empirically validate the model’s predictions by quantifying these parameters using neuroimaging and neurophysiological techniques. Investigations into how variations in brain temperature, metabolic rates, and neural efficiency affect time perception could further refine the model. Incorporating stochastic elements to account for the probabilistic nature of quantum mechanics may also enhance the model’s applicability to real-world cognitive processes.

To facilitate furtherempirical validation and integrate our model with existing neuroscientific literature, we propose potential neurobiological correlates for each parameter:

This mapping allows for direct empirical testing of the model. For example, researchers could manipulate cognitive load while measuring both neural activation and subjective time estimates. According to our model, changes in activation should correlate with distortions in perceived duration proportional to the ratio between information processed (I) and computational capacity (R).

Our model’s emphasis on temporal processing networks aligns with the “time-domain brain” framework recently proposed by Cariani and Baker (2022), which posits that the brain’s signals themselves are fundamentally composed of temporal patterns. Their framework highlights how neural spike timing serves as the raw material for information coding, describing multiple temporal representation strategies including linear, cyclical, ordinal, wave, and anticipatory time processing. This perspective complements our model by providing neurobiological mechanisms through which parameters like information processing rate (R) might be implemented. Specifically, Baker and Cariani’s emphasis on phase-locking as a “workhorse of temporal coding” and their description of neural integration windows defining temporal coincidence offers potential neural substrates for our efficiency parameter (η). Their work on temporal coherence supporting large-scale coordination further illuminates how our parameter (N) might be realized through distributed neural assemblies that maintain precise temporal relationships. Incorporating this time-domain perspective strengthens the neurobiological plausibility of our computational model and suggests additional EEG measures such as phase synchrony and cross-frequency coupling—that could serve as physiological correlates of the Perceptual Model of Time.

Building on Baker and Cariani’s (2025) “time-domain brain” framework, which formalises how time-delay networks, nested oscillatory cascades, and correlation-based wave-interference (holographic-like) processes cooperate to yield distributed, content-addressable codes. Another potential mapping of their mechanisms onto our parameters is as follows: information throughput (I) scales with the density and multiplexing of spike-time patterns; parallel processing power (N) is realised by ensembles of delay-tuned coincidence detectors whose phase-aligned outputs mutually reinforce; and energetic efficiency (η) depends on constructive interference, minimal destructive cancellation, and the metabolic savings of multiplexing. Baker & Cariani identify measurable meso-scale markers—high-order phase synchrony, cross-frequency phase-amplitude coupling, and potentially rapid microstate transitions—whose presence or absence can test whether perceptual-time dilation or compression tracks not only gross power changes but also the emergence of new carrier-mixing products and sharpened delay-specific phase relations. Thus the time-domain framework supplies concrete biophysical substrates and testable signal-level indices for every parameter of our perceptual-time model, deepening its explanatory reach and empirical falsifiability.

A complementary theoretical perspective worth considering is the controversial holographic proposal advanced by Fields et al. (2021), which conceptualizes neurons as quantum reference frames (QRFs) within an active-inference free-energy framework. This approach posits that neural ensembles implement holographic encoding wherein information exchange across a “holographic screen” between observer and environment is fundamentally classical, despite underlying quantum processes. Within this paradigm, our parameter number of processors (N) could be reinterpreted as the dimensionality of available QRFs that define measurement contexts, while efficiency (η) might reflect the thermodynamic costs of maintaining stable reference frames—costs that Fields et al. demonstrate scale with ln2NkBT. Their formalism suggests that temporal coherence emerges from phase-aligned QRFs whose stability requires energy expenditure proportional to information stored, offering a potential explanation for why higher computational loads (increased I) might distort perceptual time. Although speculative, this perspective aligns with our model by suggesting that perceptual time compression may arise when neural systems deploy additional reference frames to process complex information, thereby breaking symmetries in the underlying quantum description and inducing measurable changes in EEG coherence patterns. Future work could test this hypothesis by examining whether tasks that distort perceptual time also produce the specific cross-frequency coupling signatures predicted when additional QRFs are recruited during cognitive processing.

Moreover, theoretical work by Fields et al. (2022) reframes each neuron as a hierarchy of QRFs that must be actively stabilised “at Landauer-limited energetic cost” to support Bayesian model selection over its local micro-environment. Within this holographic, active-inference picture, the rate at which QRFs are written, erased, and refreshed sets an upper bound on the neuron’s information-throughput and, by extension, on the brain-wide processing rate (R) that is fundamental to our Perceptual Model of Time. Crucially, the maintenance of multiple, mutually-compatible QRFs is predicted to (i) elevate electrophysiological power in the beta–gamma range, (ii) shorten effective neural integration windows as decoherence accelerates, and (iii) exaggerate subjective time dilation when tasks demand finer system identification. By augmenting our EEG protocol with microstate-transition density, phase-slip counts, and fronto-parietal permutation entropy we can test whether spikes in “computational energy” reflect the hidden cost of sustaining these frames. A positive correlation between QRF-sensitive metrics, elevated R, and expanded estimates of elapsed duration would therefore provide convergent evidence that perceptual time is co-determined by both classical metabolic load and the quantum-informational bookkeeping required to keep the nervous system’s internal coordinate systems coherent.